How big is the area?
Are you removing these stones to regrade, then putting them back in place?
If just a couple tons, I would do it by hand, I have found that a concrete drag works real well for moving stone. (it looks similar to a rake with out teeth).
If it is an area larger than you'd want to do by hand a skid loader would be my next choice. I wouldn't even consider a dozer unless this is like close to or more than an acre of area.
Unless you are an experienced equipment operator, you might be money ahead to hire someone to get this moved for you. It's not always as easy as it looks.